The long gamma-ray burst GRB 191221B has abundant observations in X-ray, optical and radio bands. In the literature, the observed optical light curve of GRB 191221B displays a plateau around 0.1-day, which is rather peculiar in gamma-ray bursts.Here we performed detailed analysis of the observational data from Swift/UVOT, VLT and LCO, obtained the light curve of the multi-band afterglow of GRB 191221B. By examining optical, ultraviolet, X-ray, and radio data for this event, we demonstrate that an on-axis two-component jet model can explain the observations. Our analysis suggests that the narrow component has an initial Lorentz factor of 400 and a jet opening half-angle of 1.4 • , while the wide component has an initial Lorentz factor of 25 and a jet opening half-angle of 2.8 • . The narrow jet dominates the early decay, whereas the wider jet causes the optical plateau and dominates late decay. According to this model, the reason for the absence of the X-ray plateau is due to the steeper spectral index of the wide component, resulting in a less significant flux contribution from the wide jet in the X-ray bands than in the optical bands. Moreover, we have explained the inconsistency in the decay indices of the UVOT and Rc-band data around 2000 seconds using reverse shock emission.